Finite Group Databasebeta

← C3×#10594849 #13174387

Subgroups — C3×#10594849 #13174387

Order 1728.

1170 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64133C211yesmaximal, characteristic, complemented
2C32×C4×#67C211yesmaximal, characteristic
3C2×C32×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#63961C212yesmaximal
5C3×#63955C212yesmaximal, complemented
6C3×#63869C211yesmaximal, characteristic, complemented
7C3×#63858C212yesmaximal, complemented
8C3×#63857C211yesmaximal, characteristic, complemented
9C3×#63847C212yesmaximal, complemented
10C3×#63844C211yesmaximal, characteristic, complemented
11C3×#63841C211yesmaximal, characteristic, complemented
12C3×#5541—31nomaximal
13C3×#5513—31nomaximal
14#10594849C311yesmaximal, characteristic, direct product factor
15C22×C33×C4C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×#67C2211yescharacteristic
18C22×C32×Dic3C2212yes—
19C2×C32×C4×D3C2211yescharacteristic
20C3×#3757C2212yes—
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#3750C2212yes—
23C32×#217C2211yescharacteristic
24C32×(C2×D3)⋊C4C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2212yes—
27C32×C4⋊Dic3C2211yescharacteristic
28C32×Dic3⋊C4C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30C3×#3724C2212yes—
31C3×#3724C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×Dic32C2212yes—
37C3×Dic32C2212yes—
38C32×C4×D4—31no—
39C2×C32×C4⋊C4—31no—
40#64133C2×C311yescharacteristic, complemented
41C3×#935—32no—
42C3×#929—32no—
43C3×C4×#67—21no—
44C3×C4×#67D311yescharacteristic
45C3×C4×#67C2×C311yescharacteristic
46C3×#926—32no—
47C3×#926—31no—
48C2×C3×C4⋊Dic3—21no—
49C2×C3×C4⋊Dic3D311yescharacteristic, complemented
50C2×C3×C4⋊Dic3C2×C311yescharacteristic, complemented
51C3×#924—31no—
52C3×#924—31no—
53C3×#924—31no—
54C3×#924—61no—
55C3×#898—32no—
56C3×#897—31no—
57C3×#892—31no—
58C3×#890—31no—
59C3×#889—32no—
60C3×#889—32no—
61C3×#887—31no—
62C3×#879—32no—
63C3×#877—32no—
64C3×#870—31no—
65C3×C4×Dic6—31no—
66#63961C2×C312yes—
67#63955C2×C312yescomplemented
68#63869C2×C311yescharacteristic, complemented
69#63858C2×C312yescomplemented
70#63857C2×C311yescharacteristic, complemented
71#63847C2×C312yescomplemented
72#63844C2×C311yescharacteristic, complemented
73#63841C2×C311yescharacteristic, complemented
74C23×C33C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4—22no—
77C2×C33×C4C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C3×#634—22no—
82C32×#67—22no—
83C2×C32×Dic3—24no—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89C32×C4×D3—22no—
90C3×#552—91no—
91#5541—31no—
92#5513—31no—
93C2×C32×D4—31no—
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C22×C32×C4—32no—
98C22×C32×C4—31no—
99C22×C32×C4—41no—
100C22×C32×C4C2×D311yescharacteristic
101C22×C32×C4C2×D311yescharacteristic
102C22×C32×C4C22×C311yescharacteristic
103C2×#634C22×C311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67C2×D311yescharacteristic
106C2×C3×#67C22×C311yescharacteristic
107C22×C3×Dic3—22no—
108C22×C3×Dic3C2×D312yes—
109C22×C3×Dic3C22×C312yes—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2×D311yescharacteristic
112C2×C3×C4×D3C22×C311yescharacteristic
113C2×C3×Dic6—31no—
114C2×C3×Dic6—31no—
115C2×C3×Dic6—61no—
116C32×C4⋊C4—31no—
117C32×C4⋊C4—31no—
118C32×C4⋊C4—32no—
119C32×C4⋊C4—31no—
120C32×C22⋊C4—31no—
121C32×C22⋊C4—31no—
122C32×C42—31no—
123#3757C22×C312yes—
124C4⋊(C3⋊Dic3)C22×C311yescharacteristic
125#3750C22×C312yes—
126C3×#217—21no—
127C3×#217—32no—
128C3×#217—32no—
129C3×#217—32no—
130C3×#217—32no—
131C3×#217—62no—
132C3×#217C2×D311yescharacteristic
133C3×#217C22×C311yescharacteristic
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×(C2×D3)⋊C4C22×C311yescharacteristic
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—22no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—32no—
145C3×C4⋊Dic3—32no—
146C3×C4⋊Dic3—61no—
147C3×C4⋊Dic3C2×D312yes—
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×C4⋊Dic3C22×C311yescharacteristic
151C3×C4⋊Dic3C22×C312yes—
152C3×C4⋊Dic3C22×C311yescharacteristic
153C3×Dic3⋊C4—21no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4—32no—
161C3×Dic3⋊C4—32no—
162C3×Dic3⋊C4—62no—
163C3×Dic3⋊C4C2×D311yescharacteristic
164C3×Dic3⋊C4C22×C311yescharacteristic
165C3×C4×Dic3—21no—
166C3×C4×Dic3—32no—
167C3×C4×Dic3—32no—
168C3×C4×Dic3—32no—
169C3×C4×Dic3—32no—
170C3×C4×Dic3C2×D311yescharacteristic
171C3×C4×Dic3C22×C311yescharacteristic
172#3724C22×C312yes—
173#3724C22×C312yes—
174Dic3⋊Dic3C22×C312yes—
175Dic3⋊Dic3C22×C312yes—
176(C2×D3)⋊Dic3C22×C312yes—
177(C2×D3)⋊Dic3C22×C312yes—
178Dic32C22×C312yes—
179Dic32C22×C312yes—
180C22×C33—21no—
181C22×C33—21no—
182C22×C33#4112yes—
183C22×C33C2411yescharacteristic
184C2×C32×D3—21no—
185C2×C32×D3—21no—
186C2×C32×D3—21no—
187C33×C4—21no—
188C33×C4#4112yes—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—22no—
191C32×Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3—22no—
195C32×Dic3—21no—
196C3×#126—92no—
197C3×#125—91no—
198C3×#125—92no—
199C3×#123—92no—
200C3×C22⋊Q8—91no—
201C3×C22⋊Q8—91no—
202C3×C4×Q8—91no—
203C3×C4×D4—31no—
204C3×C4×D4—31no—
205C3×C4×D4—61no—
206C3×#117—92no—
207C3×#117—91no—
208C2×C3×C4⋊C4—31no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—61no—
211#935—32no—
212#929—32no—
213C4×#67C3×D311yescharacteristic
214#926—32no—
215#926—31no—
216C2×C4⋊Dic3C3×D311yescharacteristic, complemented
217#924—31no—
218#924—31no—
219#924—31no—
220#924—61no—
221#898—32no—
222#897—31no—
223#892—31no—
224#890—31no—
225#889—32no—
226#889—32no—
227#887—31no—
228#879—32no—
229#877—32no—
230#870—31no—
231C4×Dic6—31no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—31no—
236C23×C32—41no—
237C23×C32C22×D311yescharacteristic
238C23×C32C22×D311yescharacteristic
239C23×C32C23×C311yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C22×D311yescharacteristic
242C22×C3×D3C23×C311yescharacteristic
243C32×D4—62no—
244C2×C32×C4—22no—
245C2×C32×C4—24no—
246C2×C32×C4—22no—
247C2×C32×C4—22no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—31no—
255C2×C32×C4—31no—
256C2×C32×C4—32no—
257C2×C32×C4—31no—
258C2×C32×C4—32no—
259C2×C32×C4—41no—
260C2×C32×C4—41no—
261C2×C32×C4—42no—
262C2×C32×C4—42no—
263C2×C32×C4—44no—
264C2×C32×C4—64no—
265C2×C32×C4—62no—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C23×C311yescharacteristic
271C2×C32×C4C23×C311yescharacteristic
272C2×C3⋊Dic3C23×C312yes—
273C2×C3⋊Dic3C23×C312yes—
274#634—22no—
275C3×#67—24no—
276C3×#67—22no—
277C3×#67—22no—
278C2×C3×Dic3—24no—
279C2×C3×Dic3—24no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—44no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D312yes—
297C2×C3×Dic3C23×C312yes—
298C2×C3×Dic3C23×C311yescharacteristic
299C2×C3×Dic3C23×C311yescharacteristic
300C2×C3×Dic3C23×C312yes—
301C2×C3×Dic3C23×C311yescharacteristic
302C3×C4×D3—22no—
303C3×C4×D3—22no—
304C3×C4×D3—42no—
305C3×Dic6—62no—
306C3×Dic6—62no—
307C3×Dic6—122no—
308#552—91noSylow
309C2×C33—22no—
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C332−1+411yescharacteristic
313C32×D3—41no—
314C2×C3×Q8—91no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—61no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—32no—
322C22×C3×C4—32no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—41no—
326C22×C3×C4—61no—
327C22×C3×C4—62no—
328C22×C3×C4D3211yescharacteristic
329C22×C3×C4C2×C3×D311yescharacteristic
330C22×C3×C4C2×C3×D311yescharacteristic
331C2×#67C2×C3×D311yescharacteristic
332C22×Dic3C2×C3×D312yes—
333C2×C4×D3C2×C3×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—32no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—32no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—62no—
349C3×C4⋊C4—92no—
350C3×C4⋊C4—92no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4—92no—
354C3×C4⋊C4—91no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—92no—
362C3×C22⋊C4—92no—
363C3×C22⋊C4—92no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—61no—
367C3×C42—92no—
368C3×C42—92no—
369#217—32no—
370#217—32no—
371#217—32no—
372#217—32no—
373#217—62no—
374#217C2×C3×D311yescharacteristic
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4C2×C3×D311yescharacteristic
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—32no—
381C4⋊Dic3—32no—
382C4⋊Dic3—61no—
383C4⋊Dic3C2×C3×D311yescharacteristic
384C4⋊Dic3C2×C3×D311yescharacteristic
385C4⋊Dic3C2×C3×D312yes—
386Dic3⋊C4—32no—
387Dic3⋊C4—32no—
388Dic3⋊C4—32no—
389Dic3⋊C4—32no—
390Dic3⋊C4—32no—
391Dic3⋊C4—32no—
392Dic3⋊C4—32no—
393Dic3⋊C4—32no—
394Dic3⋊C4—62no—
395Dic3⋊C4C2×C3×D311yescharacteristic
396C4×Dic3—32no—
397C4×Dic3—32no—
398C4×Dic3—32no—
399C4×Dic3—32no—
400C4×Dic3C2×C3×D311yescharacteristic
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—22no—
404C22×C32—22no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—42no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—61no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32#23512yes—
427C22×C32#23712yes—
428C22×C32C3×#4112yes—
429C22×C32C23×D311yescharacteristic
430C22×C32C23×D311yescharacteristic
431C22×C32C24×C311yescharacteristic
432C2×C3×D3—22no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C32×C4—21no—
442C32×C4—22no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—22no—
446C32×C4—22no—
447C32×C4—22no—
448C32×C4—42no—
449C32×C4—41no—
450C32×C4—41no—
451C32×C4—42no—
452C32×C4—61no—
453C32×C4—62no—
454C32×C4—62no—
455C32×C4—61no—
456C32×C4—61no—
457C32×C4#23512yes—
458C32×C4#23712yes—
459C32×C4C3×#4112yes—
460C3⋊Dic3—22no—
461C3⋊Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—42no—
476C3×Dic3—42no—
477C3×Dic3—62no—
478C3×Dic3—62no—
479C3×Dic3—62no—
480C3×Dic3—62no—
481C3×Dic3—122no—
482C3×Dic3—122no—
483#126—92no—
484#125—91no—
485#125—92no—
486#123—92no—
487C22⋊Q8—91no—
488C22⋊Q8—91no—
489C4×Q8—91no—
490C4×D4—31no—
491#117—92no—
492#117—91no—
493C2×C4⋊C4—31no—
494C33#55211yescharacteristic, complemented, Sylow
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—31no—
499C23×C3—31no—
500C23×C3—41no—
501C23×C3—61no—
502C23×C3C2×D3211yescharacteristic
503C23×C3C22×C3×D311yescharacteristic
504C23×C3C22×C3×D311yescharacteristic
505C22×D3C22×C3×D311yescharacteristic
506C3×Q8—182no—
507C3×D4—64no—
508C3×D4—62no—
509C3×D4—62no—
510C2×C3×C4—24no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—32no—
528C2×C3×C4—31no—
529C2×C3×C4—32no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4—44no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—64no—
541C2×C3×C4—64no—
542C2×C3×C4—62no—
543C2×C3×C4—62no—
544C2×C3×C4—92no—
545C2×C3×C4—92no—
546C2×C3×C4—122no—
547C2×C3×C4—124no—
548C2×C3×C4C2×D3211yescharacteristic
549C2×C3×C4C2×D3211yescharacteristic
550C2×C3×C4C22×C3×D311yescharacteristic
551C2×C3×C4C22×C3×D311yescharacteristic
552C2×C3×C4C22×C3×D311yescharacteristic
553C2×C3×C4C22×C3×D311yescharacteristic
554#67—22no—
555C2×Dic3—24no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—32no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3C22×C3×D311yescharacteristic
563C2×Dic3C22×C3×D312yes—
564C2×Dic3C22×C3×D311yescharacteristic
565C2×Dic3C22×C3×D311yescharacteristic
566C2×Dic3C22×C3×D312yes—
567C4×D3—22no—
568Dic6—62no—
569Dic6—62no—
570Dic6—122no—
571C2×C32—22no—
572C2×C32—24no—
573C2×C32—22no—
574C2×C32—22no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32—42no—
588C2×C32—42no—
589C2×C32—44no—
590C2×C32—121no—
591C2×C32C2×#23511yescharacteristic
592C2×C32C2×#23511yescharacteristic
593C2×C32C2×#23711yescharacteristic
594C2×C32C2×#23711yescharacteristic
595C2×C32#100711yescharacteristic
596C2×C32#101011yescharacteristic
597C2×C32C2×C3×#4111yescharacteristic
598C2×C32C2×C3×#4111yescharacteristic
599C2×C32C3×2−1+411yescharacteristic
600C3×D3—42no—
601C3×D3—41no—
602C3×D3—41no—
603C2×Q8—91no—
604C2×D4—31no—
605C22×C4—32no—
606C22×C4—31no—
607C22×C4C3×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—32no—
611C4⋊C4—31no—
612C4⋊C4—92no—
613C4⋊C4—92no—
614C4⋊C4—92no—
615C4⋊C4—92no—
616C4⋊C4—91no—
617C4⋊C4—92no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—92no—
621C22⋊C4—92no—
622C22⋊C4—92no—
623C42—31no—
624C42—92no—
625C42—92no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—42no—
648C22×C3—62no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3#379512yes—
658C22×C3C3×#23512yes—
659C22×C3C3×#23712yes—
660C22×C3C22×D3211yescharacteristic
661C22×C3C23×C3×D311yescharacteristic
662C22×C3C23×C3×D311yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—62no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—121no—
689C3×C4—122no—
690C3×C4—122no—
691C3×C4—121no—
692C3×C4—182no—
693C3×C4—182no—
694C3×C4#380412yes—
695C3×C4C3×#23512yes—
696C3×C4C3×#23712yes—
697Dic3—21no—
698Dic3—21no—
699Dic3—22no—
700Dic3—22no—
701Dic3—21no—
702Dic3—62no—
703Dic3—62no—
704Dic3—62no—
705Dic3—62no—
706Dic3—122no—
707Dic3—122no—
708C32—21no—
709C32—21no—
710C32—21no—
711C32—41no—
712C32#551311yescharacteristic, complemented
713C32#554111yescharacteristic, complemented
714C32C3×#55211yescharacteristic, complemented
715C23—31no—
716C23C2×C3×D3211yescharacteristic
717Q8—182no—
718D4—62no—
719C2×C4—22no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—92no—
728C2×C4—92no—
729C2×C4C2×C3×D3211yescharacteristic
730C2×C4C2×C3×D3211yescharacteristic
731C2×C3—24no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—22no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—42no—
745C2×C3—42no—
746C2×C3—44no—
747C2×C3—41no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—122no—
751C2×C3—121no—
752C2×C3—121no—
753C2×C3C2×#379511yescharacteristic
754C2×C3#6429711yescharacteristic
755C2×C3C2×#380411yescharacteristic
756C2×C3C2×C3×#23511yescharacteristic
757C2×C3C2×C3×#23511yescharacteristic
758C2×C3C2×C3×#23711yescharacteristic
759C2×C3C2×C3×#23711yescharacteristic
760C2×C3C3×#100711yescharacteristic
761C2×C3C3×#101011yescharacteristic
762D3—41no—
763C22—21no—
764C22—21no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22C3×#379512yes—
769C22C22×C3×D3211yescharacteristic
770C4—21no—
771C4—61no—
772C4—62no—
773C4—62no—
774C4—61no—
775C4—61no—
776C4—182no—
777C4—182no—
778C4C3×#380412yes—
779C3—21no—
780C3—21no—
781C3—21no—
782C3—41no—
783C3#1059484911yescharacteristic, direct product factor
784C3C3×#551311yescharacteristic, complemented
785C3C3×#554111yescharacteristic, complemented
786C2—22no—
787C2—121no—
788C2C2×C3×#379511yescharacteristic
789C2C3×#6429711yescharacteristic
790C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC2×C32×#67C22
hypercenterC22×C3×C4D32
hypocenterC32C3×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#64133C2semidirect
3. C2×C32×C4⋊Dic3C2semidirect
5. C3×#63955C2semidirect
6. C3×#63869C2semidirect
7. C3×#63858C2semidirect
8. C3×#63857C2semidirect
9. C3×#63847C2semidirect
10. C3×#63844C2semidirect
11. C3×#63841C2semidirect
14. #10594849C3direct (N × H)
40. #64133C2×C3semidirect
49. C2×C3×C4⋊Dic3D3semidirect
50. C2×C3×C4⋊Dic3C2×C3semidirect
67. #63955C2×C3semidirect
68. #63869C2×C3semidirect
69. #63858C2×C3semidirect
70. #63857C2×C3semidirect
71. #63847C2×C3semidirect
72. #63844C2×C3semidirect
73. #63841C2×C3semidirect
216. C2×C4⋊Dic3C3×D3semidirect
494. C33#552semidirect
712. C32#5513semidirect
713. C32#5541semidirect
714. C32C3×#552semidirect
783. C3#10594849direct (N × H)
784. C3C3×#5513semidirect
785. C3C3×#5541semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#641332
C32×C4×#672
C2×C32×C4⋊Dic32
C3×#639612
C3×#639552
C3×#638692
C3×#638582
C3×#638572
C3×#638472
C3×#638442
C3×#638412
C3×#55413
C3×#55133
#105948493